Internal problem ID [4121]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined
Coefficients
Problem number: Exercise 21.32, page 231.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-5 y^{\prime }+6 y-{\mathrm e}^{x} \left (2 x -3\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 13
dsolve([diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=exp(x)*(2*x-3),y(0) = 1, D(y)(0) = 3],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{2 x}+x \,{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 35
DSolve[{y''[x]-5*y'[x]-6*y[x]==Exp[x]*(2*x-3),{y[0]==1,y'[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{175} e^{-x} \left (-7 e^{2 x} (5 x-9)+87 e^{7 x}+25\right ) \\ \end{align*}